User talk:Xenwolf: Difference between revisions

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: Hardly this time, but it depends on whether there are concrete questions to answer (easy), to discuss topics in their full breadth (hard), or to make glyphs (impossible). For me it's still unclear how your approach relates to [[205edo]] one of Hunt. Did you have a look on it (41x5 leads to a system with a perfect 3-limit approximation and very good to fair approximations of other limits)? --[[User:Xenwolf|Xenwolf]] ([[User talk:Xenwolf|talk]]) 14:28, 8 October 2020 (UTC)

:: Okay, firstly, the steps of [[205edo]] are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with [[24edo]] on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Is there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:02, 8 October 2020 (UTC)

:: Okay, firstly, the steps of [[205edo]] are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with [[24edo]] on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Are there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --[[User:Aura|Aura]] ([[User talk:Aura|talk]]) 16:02, 8 October 2020 (UTC)

Revision as of 16:24, 8 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary ← Older edit		Revision as of 16:39, 8 October 2020 view source Aura (talk \| contribs) autopatrolled, emailconfirmed 5,920 edits No edit summary Newer edit →
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	: Hardly this time, but it depends on whether there are concrete questions to answer (easy), to discuss topics in their full breadth (hard), or to make glyphs (impossible). For me it's still unclear how your approach relates to [[205edo]] one of Hunt. Did you have a look on it (41x5 leads to a system with a perfect 3-limit approximation and very good to fair approximations of other limits)? --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 14:28, 8 October 2020 (UTC)		: Hardly this time, but it depends on whether there are concrete questions to answer (easy), to discuss topics in their full breadth (hard), or to make glyphs (impossible). For me it's still unclear how your approach relates to [[205edo]] one of Hunt. Did you have a look on it (41x5 leads to a system with a perfect 3-limit approximation and very good to fair approximations of other limits)? --[[User:Xenwolf\|Xenwolf]] ([[User talk:Xenwolf\|talk]]) 14:28, 8 October 2020 (UTC)

	:: Okay, firstly, the steps of [[205edo]] are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with [[24edo]] on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Is there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 16:02, 8 October 2020 (UTC)		:: Okay, firstly, the steps of [[205edo]] are a bit too small, and are likely to blend into one another, whereas 159edo doesn't have that problem as the step size is greater than 7 cents. In comparing the patent vals up to the 17-limit, I can see that the approximations of the 3-limit, 7-limit and 11-limit in [[159edo]] are superior to those of 205edo in terms of absolute error, though the reverse is true when it comes to the 5-limit, the 13-limit and the 17-limit. Considering that the 3-limit is the major diatonic navigational prime for the main key signatures, while the 11-limit is the major paradiatonic navigational prime for things like quartertone key signatures, and that both of these prime limits are significant for the many microtonalists who end up starting with [[24edo]] on account of 24edo being perhaps one the best known microtonal systems, I'd say that 159edo's better performance in these limits is a major factor to be considered, as are the issues with 205edo's smaller stepsize. Are there any other facets of the relationship between my approach to 159edo and Hunt's approach to 205edo that you wish to know about? --[[User:Aura\|Aura]] ([[User talk:Aura\|talk]]) 16:02, 8 October 2020 (UTC)